Linear Frequency Modulation Research Articles

Symmetry Feature Estimation Over STFT Transform to Improve Radar Classification Based on the Wisard Weightless Neural Network

Automated early recognition of enemy radar emissions are essential for the survival of a warship. Radar signals intercepted by a passive digital Electronic Support Measure (ESM) receiver can be classified based on the type of intrapulse modulation. The modulation classification is typically based on features extracted from the preprocessed radar’s signal. Low Probability of Intercept (LPI) radars can use phase or frequency modulated signals to make radar emissions difficult for the enemy to detect. This paper proposes the use of a new feature, the symmetry measured in a Time-Frequency (TF) matrix, to improve intrapulse radar modulation classification. The analysis of the symmetry in a STFT matrix is characterized by an image processing problem, where the matrix is interpreted as a grayscale image. This paper also proposes the use of Weightless Neural Network WiSARD in identifying symmetry patterns in the Short Time Fourier Transform (STFT) matrix, a characteristic present in signals with Barker and Polytime phase modulations and which can be used by classifiers to discriminate them from signals with other types of modulations such as polyphase modulations (P1, P2, P3, P4 and Frank), linear frequency modulation (LFM), and Non Linear Frequency Modulation.

Multi-band reconfigurable microwave photonic transceiver towards high-performance integrated radar.

As an effective approach to overcome the electronic bottlenecks of conventional electrical radars, microwave photonic radars have demonstrated significant superiority in their perception and recognition capabilities. However, trade-offs exist among the reconfigurability, signal time-bandwidth product (TBWP), linearity, and phase coherence of current photonic radars, which ultimately weaken the overall performance. To address these challenges, a photonic transceiver based on electrically assisted synchronized lasers is proposed and demonstrated, which combines high resolution and multi-band reconfigurability. Optical coherent heterodyne linear frequency-modulated (LFM) radar signal generation and photonic dechirping reception are implemented through the synchronized lasers at the transmitter and receiver, respectively. In a proof-of-concept experiment, reconfigurable LFM signals covering the L- to Ka-band with improved linearity and phase coherence are generated. Furthermore, the proposed photonic transceiver operates in the Ka-band with an ultra-large signal TBWP of 4 × 106, enabling high-resolution ranging and inverse synthetic aperture radar (ISAR) imaging. A range resolution of 1.92 cm and an imaging resolution of 1.92 cm × 1.89 cm are obtained, which require a receiver sampling rate of only 5 MSa/s. Featuring a simple structure, flexible reconfiguration, and integration compatibility, the demonstrated photonic transceiver opens new opportunities for next-generation miniaturized radar application scenarios.

Design of an Underwater Acoustic Waveform and Integrated System for Communication and Detection

Combining underwater communication and detection can reduce system size and power consumption as well as improve secrecy. This paper presents a waveform that integrates continuous phase modulation (CPM) for data communication with linear frequency modulation (LFM) for detection. It is shown that the velocity ambiguity and range performance with this waveform are similar to those with only LFM. An integrated underwater acoustic system is also proposed to achieve simultaneous communication and detection. A symbol suffix (SS) is introduced into the signal frame at the transmitter and a two-step algorithm is employed at the receiver for frequency and phase offset estimation. Results are presented, showing that this decreases the sensitivity to CPM and reduces the range ambiguity side lobes. Further, the proposed system can effectively recover the data from the received signal. The bit error rate (BER) is shown to be better than that of traditional systems without a symbol suffix. With changes in the signal-to-noise ratio (SNR), the bit error rate (BER) in underwater acoustic environments is comparable to that in an additive white Gaussian noise (AWGN) channel, indicating a significant improvement in communication performance within the underwater acoustic channel.

Autoencoder-Based DIFAR Sonobuoy Signal Transmission and Reception Method Incorporating Residual Vector Quantization and Compensation Module: Validation Through Air Channel Modeling

This paper proposes a novel autoencoder-based neural network for compressing and reconstructing underwater acoustic signals collected by Directional Frequency Analysis and Recording sonobuoys. To improve both signal compression rates and reconstruction performance, we integrate Residual Vector Quantization and a Compensation Module into the decoding process to effectively compensate for quantization errors. Additionally, an unstructured pruning technique is applied to the encoder to minimize computational load and parameters, addressing the battery limitations of sonobuoys. Experimental results demonstrate that the proposed method reduces the data transmission size by approximately 31.25% compared to the conventional autoencoder-based method. Moreover, the spectral mean square errors are reduced by 60.58% for continuous wave signals and 55.25% for linear frequency modulation signals under realistic air channel simulations.

A Submicrosecond-Response Ultrafast Microwave Ranging Method Based on Optically Generated Frequency-Modulated Pulses.

An ultrafast microwave ranging method based on optically generated frequency-modulated microwave pulses is proposed in this study. The theoretical analysis demonstrated that nanosecond-scale linear frequency modulation microwave pulse can be obtained by femtosecond laser interference under the condition of unbalanced dispersion, which can be used to achieve a high temporal resolution of the displacement change in the measurement by the principle of frequency modulation continuous wave (FMCW) radar. The proof-of-principle experiment successfully measured the displacement change with an error of 2.5 mm and a range of 0.6 m, with a response time of 468 ns. Compared to existing microwave ranging technologies, the temporal resolution was improved by two orders of magnitude, which greatly improves the temporal resolution of distance measurement in the field of microwave FMCW radar.

Efficient hardware implementation of ROM-free LFM waveform generation for real-time reconfigurable software-defined radar

Abstract This paper presents a novel method for generating Linear Frequency Modulation (LFM) waveforms. Conventional Look-Up Table (LUT)-based method require large storage resources, especially in high-resolution, multi-mode radar systems. To address this issue, we propose a ROM-free, real-time LFM waveform generator. It uses the fourth-order Runge-Kutta (RK-4) method to solve differential equations for the in-phase and quadrature components. The proposed approach dynamically generates LFM waveforms using only parameters such as pulse width, bandwidth, and sampling rate, eliminating the need for pre-calculated waveforms and LUTs. This method completely removes storage requirements, enabling faster synthesis times and achieving minimal latency. The generator’s performance is validated through simulation and FPGA implementation using a full hardware description language. Results confirm its effectiveness, making it a strong candidate for advanced radar systems that demand high performance with limited hardware resources.

New Wigner Distribution and Ambiguity Function for the Offset Fractional Fourier Transform and Their Applications

ABSTRACTThis paper introduces the new offset fractional Fourier Wigner distribution and offset fractional Fourier ambiguity function (OFrWD and OFrAF). Moreover, many various useful properties of them are also derived. Besides, convolutions via offset fractional Fourier transform are also introduced. Furthermore, the relationships between proposed convolutions and the OFrWD as well as OFrAF are also obtained. In addition, with the help of simulation, applications of OFrWD and OFrAF are established, such as designing multiplicative filters in the offset fractional Fourier transform (OFrFT) domain and detecting the parameters of single‐component and multicomponent linear frequency‐modulated (LFM) signals.

All-fiber fast coherent LiDAR for ranging and velocimetry based on optical comb injection

Frequency-modulated continuous-wave light detection and ranging (LiDAR) is a powerful ranging technique that offers inherent resistance to ambient light and the capability to simultaneously measure both distance and velocity. However, conventional LiDAR systems often face challenges with environmental interference and achieving a balance between demodulation complexity, data-refresh rate, and precision. Here, we introduce an all-fiber LiDAR system that utilizes optical comb injection for high-precision ranging and velocimetry. Owing to the injection locking process, the beam output from slave lasers inherits the linear and fast frequency modulation features of the injected optical comb sidebands generated through an electro-optics modulator while maintaining a stable output power with little phase noise, solving a big concern in traditional external modulation schemes. The unique dual-sideband locking and common-path design enhance stability and anti-interference ability, enabling the system to possess a high data-refresh rate of over 10 kHz and a high precision of 500 μm without complex algorithms or compensation circuits. Dynamic ranging and imaging of noncooperative targets are also demonstrated. With the advantages of fast and noncontact measurement, high precision and stability, and anti-interference ability, the proposed system has potential applications in automatic driving, machine control, and intelligent robotics.

Performance Analysis of Troposphere Scattering Communication Channel with Chirp-BOK Modulation.

By utilizing chirp-BOK (binary orthogonal keying) modulation into a troposphere scattering communication system, a lower demodulation threshold can be achieved with excellent linear frequency modulation properties in a strong noise and weak signal environment. Firstly, the bit error rate (BER) formula of chirp-BOK modulation over a Rayleigh fading channel was derived theoretically. Then, the BER performance with different chirp-BOK parameters were numerically calculated. In order to investigate the performance of chirp-BOK over deeping fading troposphere scattering link, a seven-path equal-delay Rayleigh fading model was employed. Finally, the system BER performance was simulated under different tap delay and time-bandwidth product parameters. The results demonstrate that when BER reaches 10-4, the optimal configuration of the system achieves a gains approximately from 1.7 dB to 10 dB compared to non-optimized configuration under different Path-Gain-Vector with varying tap delays.

Photonics-assisted analog windowing and matched filtering.

In this paper, we propose an integrated method for windowing and matched filtering in the analog domain based on microwave photonic technology, which utilizes dispersion regulation of optical waveguide to achieve the windowing processing of broadband signals in the optical domain and the surface acoustic wave filter (SAWF) to achieve the following matched filtering processing in the radio frequency (RF) domain, thus realizing their integration processing in the analog domain. The proposed method is validated by simulation and experiment, in which the integrated processing of matched filtering and windowing in the analog domain for a linear frequency modulation (LFM) signal with a bandwidth of 1 GHz is carried out and the peak to sidelobe ratio (PSLR) of the output signal is -19.55 dB and the mainlobe width (MLW) broadens to 0.16 ns with the maximum achievable dispersion value. The proposed method can significantly reduce the pressure of signal processing at the back-end of the radar system and improve the response speed of the broadband radar system in detecting the targets.

Joint radar and communication based on piece-wised LFM signals

Abstract Existing joint radar detection and communication(JDC) systems suffer from high peak-to-average power ratio(PAPR) or distance blind spot zones. In this paper, we present a novel JDC system based on piece-wised linear frequency modulation(LFM) signals. Based on the proposed piece-wised LFM modulation signal, the novel JDC system can achieve linear frequency modulation continuous wave(LFMCW) detection, and the PAPR and blind zone issues are solved. Besides, spread spectrum communication can be simultaneously conducted with the same modulation signal. Simulation results show that the proposed JDC system has similar detection performance to the traditional sawtooth LFMCW detection scheme, and the bit-error rate of communication is less than 10−6 when the the bit rate is 500kbps and the signal-to-noise ratio is 10 dB.

Radar and communication integration under FPGA platform: real-time waveform generation with time division multiplexing and waveform sharing strategy

Abstract The integration of radar and communication technologies is gaining prominence in electronic information systems. This paper explores advanced waveform strategies—LFM (Linear Frequency Modulation) + MSK (Minimum Shift Keying) based on time-division multiplexing and LFM-MSK utilizing waveform sharing. These methods enhance spectrum efficiency and system capabilities in detecting targets and transmitting data reliably amidst complex environments. Based on the FPGA (Field Programmable Gate Array) platform, this study proposes real-time waveform generation methods for integrated radar communication waveforms, specifically LFM+MSK and LFM-MSK. It focuses on discussing FPGA implementation solutions for these methods and validates their effectiveness. This research addresses a critical gap in the field and provides practical insights for radar communication integration systems.

Near-Field Target Detection Method for Vortex Electromagnetic Wave Radar based on Modal Baseline

Abstract Vortex electromagnetic (EM) waves can provide more target information, which is orbital angular momentum (OAM), than traditional plane waves in the field of radar detection. By emitting multiple different OAM modes of vortex EM waves to the same target, the azimuth information of the target can be obtained. The Linear Frequency Modulated (LFM) radar is often used in current OAM radar design. At present, researches on vortex EM wave imaging usually requires the emission of a large number of OAM modes to irradiate the target. Although many achievements have been made to significantly reduce this number, it is often accompanied by problems such as loss of azimuth imaging accuracy or poor real-time performance in practical applications. In response to this issue, this paper proposes a near-field target detection method based on modal baseline using vortex EM waves. By alternately emitting vortex EM waves with least OAM mode difference of 1, the method achieves range-velocity imaging while the OAM mode phase information is not blurred. The target detection task is carried out in the range-Doppler dimension, avoiding the problem of azimuth imaging. Through signal processing, our method achieves 3d point cloud detection of target velocity, range, and azimuth. Simulation results compared with traditional phase comparison azimuth measurement method proved the superiority of our method. The work and results provide suggestions to the development of vortex EM wave target detection.

Алгоритм обнаружения зондирующих сигналов с линейной частотной модуляцией на основе нейросетевой обработки их спектров на выходе автокорреляционной схемы

The article discusses the features of usage the neural network approach in the problem of detecting signals with linear frequency modulation at the output of an autocorrelation scheme. The results demonstrate significantly reduce the number of false alarms compared to the traditional method based on threshold processing.

Fast Parameter Estimation of Linear Frequency Modulation Signals in Marine Environments Based on Gradient Optimization Strategy

Multi-buoy sonar systems achieve target localization by receiving broadband Linear Frequency Modulation signals emitted from the transmitter. Accurate estimations of the parameters of Linear Frequency Modulation signals significantly enhance the localization accuracy. Linear Frequency Modulation signals can be focused into the fractional domain through Fractional Fourier Transform, but this increases the computational complexity. In marine environments, the low signal-to-noise ratio and multipath effects degrade the parameter estimation accuracy further. To address these issues, this paper proposes a fast estimation algorithm based on the Fractional Fourier Transform and a Gradient Subtraction-Average-Based Optimizer. This algorithm leverages the impulsive characteristics of Linear Frequency Modulation signals after Fractional Fourier Transform transformation, using the Fractional Fourier Transform as the fitness function. The Gradient Subtraction-Average-Based Optimizer algorithm includes three enhancement strategies: chaotic mapping initialization, a Golden Sine Algorithm, and an adaptive t-distribution variational operator. The simulation results demonstrate that the Gradient Subtraction-Average-Based Optimizer algorithm improves the issues of low diversity in the search agents, imbalanced global and local search capabilities, and susceptibility to local optima. A comparative analysis and statistical testing confirm that under a low signal-to-noise ratio and multipath effect conditions, the Gradient Subtraction-Average-Based Optimizer algorithm not only ensures real-time parameter estimation but also improves the estimation accuracy. The results of the parameter estimation provide reliable data support for subsequent target localization.

Deception Jamming Method for Wideband Linear Frequency Modulation Radar Based on Time-Modulated Array

Deception Jamming Method for Wideband Linear Frequency Modulation Radar Based on Time-Modulated Array

An Anti-Interference Method Based on Energy Residual Searching in GNSS Positioning Applications

Addressing the issue of linear frequency modulation (LFM) interference in GNSS positioning, this paper proposes an interference suppression method based on energy residual searching, incorporating the fractional Fourier transform (FrFT) for improved performance. In GNSS systems, LFM interference can severely impair positioning accuracy and system robustness, potentially rendering the receiver incapable of performing accurate localization. To address this issue, an energy residual function is introduced to quantitatively assess the impact of interference on the original signal. This function combines differences in signal energy with signal quality after spectral line removal to achieve effective interference evaluation. By optimizing the parameters of the fractional Fourier transform to maximize the value of the energy residual function the proposed method significantly enhances interference suppression. Our experimental results demonstrate that the method performs exceptionally well on practical datasets, effectively removing interference and restoring relevant peaks. This approach mitigates the negative effects of LFM interference on GNSS positioning performance, substantially improving both positioning accuracy and system robustness.

Analyzing Pulse Compression Performance and Image Quality Metrics of Different Excitations in MAET With Magnetic Field Measurements.

This study investigates the pulse compression technique to improve the performance of magneto-acousto-electrical tomography (MAET) with magnetic field measurements through numerical studies. Emphasizing the effects of specific coil configuration on MAET measurements, the study conducts evaluations using a linear phased array (LPA) transducer and numerical breast models with tumor inclusion. It provides feasibility and a detailed comparative analysis of various excitations, including linear frequency modulated (LFM), Barker code, and Golay code excitations in MAET. To simulate experimental conditions, additive White Gaussian noise is added to the MAET signal detected by the receiver coils. The results obtained from the LPA steering angle at 0° and the reconstructed B-mode MAET images using the pulse compression technique lead to improvements compared with conventional single-cycle excitation. The computed mean signal-to-noise ratio (SNR) improvements for LFM, Barker code, and Golay code excitations in B-mode MAET images for 10,000 iterations are 7.42, 8.36, and 8.44 dB, respectively, compared with single-cycle excitation. Similarly, the mean contrast-to-noise ratio (CNR) improvements for these excitations in B-mode MAET images are 1.43, 1.63, and 1.9 dB, respectively. The results demonstrate that Golay code is superior in CNR and image quality metrics, while Golay and Barker codes have comparable SNR and outperform LFM. The research shows that the coil configuration significantly impacts tumor detection. With Golay code excitation, detecting a tumor as small as 5 mm × 2 mm at a depth of 33 mm with an SNR of 6.38 dB is possible, achieving an axial resolution of 2 mm.

Seamless Optimization of Wavelet Parameters for Denoising LFM Radar Signals: An AI-Based Approach

Linear frequency modulation (LFM) signals are pivotal in radar systems, enabling high-resolution measurements and target detection. However, these signals are often degraded by noise, significantly impacting their processing and interpretation. Traditional denoising methods, including wavelet-based techniques, have been extensively used to address this issue, yet they often fall short in terms of optimizing performance due to fixed parameter settings. This paper introduces an innovative approach by combining wavelet denoising with long short-term memory (LSTM) networks specifically tailored for LFM signals in radar systems. By generating a dataset of LFM signals at various signal-to-noise Ratios (SNR) to ensure diversity, we systematically identified the optimal wavelet parameters for each noisy instance. These parameters served as training labels for the proposed LSTM-based architecture, which learned to predict the most effective denoising parameters for a given noisy LFM signal. Our findings reveal a significant enhancement in denoising performance, attributed to the optimized wavelet parameters derived from the LSTM predictions. This advancement not only demonstrates a superior denoising capability but also suggests a substantial improvement in radar signal processing, potentially leading to more accurate and reliable radar detections and measurements. The implications of this paper extend beyond modern radar applications, offering a framework for integrating deep learning techniques with traditional signal processing methods to optimize performance across various noise-dominated domains.

Signal Processing for Novel Noise Radar Based on de-chirp and Delay Matching.

Modern radar technology requires high-quality signals and detection performance. However, traditional frequency-modulated continuous wave (FMCW) radar often has poor anti-jamming capabilities, and the high sampling rates associated with large time-bandwidth product signals can lead to increased system hardware costs and reduced data processing efficiency. This paper constructed a composite radar waveform based on noise frequency modulation (NFM) and linear frequency modulation (LFM) signals, enhancing the signal's complexity and anti-jamming capability. Furthermore, a method for optimizing the processing of echo signals based on de-chirp and delay matching is proposed. The locally generated LFM signal is used to de-chirp the received echoes, resulting in a narrowband difference frequency noise signal. Subsequently, delay matching is performed in the fast time domain using the locally generated NFM signal according to the number of sampling points in the traversal processing period, allowing for the acquisition of target delay information. While reducing the analog-to-digital (A/D) sampling rate, the detection performance for wideband echo signals under high sampling rates is still maintained, with sidelobe levels and range resolution preserved. Accumulating this information in the slow time domain enables accurate target detection. The effectiveness of the proposed method is validated through simulation experiments.